GATE CS 2015 Set 2 — Question 13
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Engineering Mathematics → Sets & Combinatorics → Sets, Relations & Functions
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Question
Let be the relation on the set of positive integers such that if and only if and are distinct and have a common divisor other than 1. Which one of the following statements about is true?
Correct answer
(D) R is symmetric but not reflexive and not transitive
Solution
holds iff and .
- Reflexive? No. would need , which never holds.
- Symmetric? Yes. If and , then and .
- Transitive? No. Take , , : (common divisor 2) and (common divisor 3), but , so is false.
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